Use the power series Σ 2(-1)^x^, \x| < 1 1 + x n = 0 to find a power series for the function, centered at 0. f(x) = In(x + 1 dx x + 1 f(x) Σ n = 0 Determine the interval of convergence. (Enter your answer

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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Correct answer please 2 part question
Use the power series
00
1
(-1)"x", \x| < 1
n = 0
1 + x
to find a power series for the function, centered at 0.
f(x)
= In(x + 1) =
dx
X + 1
00
f(x) =
Σ
n = 0
Determine the interval of convergence. (Enter your answer using interval notation.)
Transcribed Image Text:Use the power series 00 1 (-1)"x", \x| < 1 n = 0 1 + x to find a power series for the function, centered at 0. f(x) = In(x + 1) = dx X + 1 00 f(x) = Σ n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)
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